Distributed Raman Amplification (DRA) is known by those of ordinary skill in the art. DRA is a powerful technique to improve the optical signal to noise ratio (OSNR) margin in a transmission optical fiber of long-haul Wavelength Division Multiplexing (WDM) systems, for example. The principle of the Raman amplifier is based on the stimulated emission process associated with Raman scattering in fiber for amplification of the signal. In quantum mechanics, Raman scattering is a process in which an incident photon excites an electron to a virtual state and then the stimulated/spontaneous emission occurs when the electron de-excites down to the upper photon energy level of the glass molecule of the optical fiber. In amorphous materials such as fused silica, molecular vibrational frequencies spread into bands that overlap and create a continuum. As a result, the Raman gain spectrum extends over a relatively large frequency range that is offset from the pump light frequency (up to 40 THz) with a broad peak located near 13.2 THz. Optical fibers can act as a broadband amplifier because of this feature.
A Raman pump is included as part of an amplifier and injects light into the fiber in the opposite direction of the source signal. The injected photons boost the optical signal where it is most needed—at the far end of the fiber where the signal is experiencing the most attenuation.
Referring now to FIG. 1, the energy levels and transitions associated with stimulated and spontaneous Raman emissions are shown. Generally, the available flat gain bandwidth for a single pump is about 15 nanometers (nm). To realize ultra-broadband (e.g., greater than about 75 nm, covering both C-band and L-band) amplification, pump lights (also referred to as pump lasers) with multiple wavelengths (typically greater than four) are necessary. In addition, to reduce the crosstalk caused by both pump power fluctuation and signal-induced pump depletion, it is advantageous to make the pump lights counter-propagating with the signals. In a multi-wavelength counter-pumped Raman fiber amplifier, it has been found that the noise performance in the shorter wavelength band is significantly worse than the noise performance in the longer wavelength band. This is due to temperature-dependent spontaneous Raman emission, the proximity of the signal to the pumps and rapid energy transfer of shorter-wavelength pumps to the longest-wavelength pump.
To flatten the noise performance in a multiple-wavelength pumped Raman fiber amplifier, a bidirectional-pumping scheme using specially designed pump lasers with very low relative intensity noise is used. A nearly 2 dB noise figure (NF) improvement was obtained in the shorter wavelength band by use of this scheme. For such a scheme, however, the crosstalk originating from signal-induced co-propagating pump depletions is still serious and is difficult to overcome.
The origin of noise degradation in broadband signal transmission systems will now be described. A counter-pumped Raman fiber amplifier includes M pumps (P1, . . . , PM). The set of propagation equations governing forward signal light power evolution considering temperature-dependent spontaneous Raman emission is given by Equation 1 below:
                                                        ⅆ                                                S                  n                                ⁡                                  (                  z                  )                                                                    ⅆ              z                                =                                                                      B                  n                                ⁡                                  (                  z                  )                                            ⁢                                                S                  n                                ⁡                                  (                  z                  )                                                      +                                          C                n                            ⁡                              (                z                )                                      -                                          α                n                            ⁢                                                S                  n                                ⁡                                  (                  z                  )                                                                    ⁢                                  ⁢                                            B              n                        ⁡                          (              z              )                                =                                    ∑                              j                =                1                            M                        ⁢                                                  ⁢                                                            g                  nj                                                  2                  ⁢                                      A                    eff                                                              ⁢                                                P                  j                                ⁡                                  (                  z                  )                                                                    ⁢                                  ⁢                                            C              n                        ⁡                          (              z              )                                =                                    ∑                              j                =                1                            M                        ⁢                                                  ⁢                                                                                g                    nj                                                        2                    ⁢                                          A                      eff                                                                      ⁡                                  [                                                            hv                      n                                        ⁢                    Δ                    ⁢                                                                                  ⁢                                          v                      ⁡                                              (                                                  1                          +                                                      1                                                                                          e                                                                                                      h                                    ⁡                                                                          (                                                                                                                        ϛ                                          j                                                                                -                                                                                  v                                          n                                                                                                                    )                                                                                                        ⁢                                                                      /                                                                    ⁢                                  κT                                                                                            -                              1                                                                                                      )                                                                              ]                                            ⁢                                                P                  j                                ⁡                                  (                  z                  )                                                                                        (        1        )            where αn denotes the fiber loss at signal light frequency Vn,  denotes the frequency of the j th pump light, Sn denotes the nth input signal and Z denotes fiber length. The subscript n denotes the nth signal, and gnj is the Raman gain coefficient. Aeff is the fiber effective area. The term of
  1  +      1                  e                              h            ⁡                          (                                                ϛ                  j                                -                                  v                  n                                            )                                ⁢                      /                    ⁢          κT                    -      1      denotes the temperature-dependent spontaneous Raman emission factors, where h is the Plank's constant, κ is Boltzman's constant, T is the temperature in Kelvin, and Δv is the noise bandwidth. In Equation 1, signal—signal Raman interaction and Rayleigh scattering have not been taken into account. The pump light power evolution has a similar equation as Equation 1. The signal gain Gn(L) and noise power Θn(L) at the fiber output end corresponding to Equation 1 are given by
                                                        G              n                        ⁡                          (              L              )                                =                      exp            ⁢                          {                                                                    -                                          α                      n                                                        ⁢                  L                                +                                                      ∫                    0                    L                                    ⁢                                                                                    B                        n                                            ⁡                                              (                        z                        )                                                              ⁢                                                                                  ⁢                                          ⅆ                      z                                                                                  }                                      ⁢                                  ⁢                                            Θ              n                        ⁡                          (              L              )                                =                                                    ∫                0                L                            ⁢                                                                    C                    n                                    ⁡                                      (                    z                    )                                                  ⁢                                                                            G                      n                                        ⁡                                          (                      L                      )                                                                                                  G                      n                                        ⁡                                          (                      z                      )                                                                      ⁢                                                                  ⁢                                  ⅆ                  z                                                      =                                          ∫                0                L                            ⁢                                                                    C                    n                                    ⁡                                      (                    z                    )                                                  ⁢                                                      G                    n                                    ⁡                                      (                                          z                      ,                      L                                        )                                                  ⁢                                  ⅆ                  z                                                                                        (        2        )            where Gn(z, L) means signal gain obtained from z to L. From the above, it can be seen that the noise power is dependent on both the noise generation factor Cn(z) and the longitudinal gain spectrum profile Gn(z). Gn(z) is assumed to be identical for various signal light frequencies. When the signal light frequency is closer to the pump light frequencies, i.e., the value of j −vn becomes smaller, the value of Cn(z), and hence the noise power Θn(L), increases accordingly. This is due to the fact that the temperature-dependent spontaneous Raman emission factor,
      1    +          1                        e                                    h              ⁡                              (                                                      ϛ                    j                                    -                                      v                    n                                                  )                                      ⁢                          /                        ⁢            κT                          -        1              ,increases when j −vn becomes smaller. For example, if T=300, while j −vn=13.2 THz (corresponding to a peak Raman shift, a large frequency difference between the pump and the signal) and 1 THz (corresponding to a small frequency difference between the pump and the signal), the value of
  1  +      1                  e                              h            ⁡                          (                                                ϛ                  j                                -                                  v                  n                                            )                                ⁢                      /                    ⁢          κT                    -      1      becomes 1.125 and 5.55, respectively. This shows that the impact of temperature-dependent spontaneous Raman emission on signals in the shorter-wavelength side is much more serious than that in the longer-wavelength side.
The impact of the longitudinal gain spectrum profile Gn(z) also should be considered. From Equation 2 it can be seen that, for the same value of Gn(L), the value of Θn(L) increases when the gain seen by the signal is closer to the output end of the fiber. Physically, this is due to different mechanisms for noise generation and signal amplification. Noise is generated along the fiber length. Moreover, from Equation 1 it can be seen that the noise generation factor Cn(z) has a linear relationship with the pump light power. However, the longitudinal gain spectrum profile Gn(z) has an exponential relationship with the pump light power. This implies that the noise generation is more distributed along the fiber length than is the signal gain. As a result, when the signal gain is closer to the output end of the fiber, most of the noise components generated along the fiber length will experience a relatively large gain and, hence, result in a worse noise performance; however, when the signal gain is farther away from the output end of the fiber, there are relatively fewer noise components that experience large gain and, hence, the result is enhanced noise performance.
FIGS. 2a–2c give a simulated example of a conventional five-wavelength counter-pumped fiber Raman amplifier. The powers and wavelengths of the five pumps used are: 1421 nm (520 mw), 1435 nm (400 mW), 1450 nm (190 mW), 1472 nm (58 mW) and 1501 nm (98 mW). The input signal power is chosen to be −15 dBm/channel and 80 km of Stranded Single-Mode Fibers (SSMF) is used in the simulations. The fiber loss curve 5 is shown in FIG. 3. The fiber effective area is approximately 80 μm2.
FIGS. 2b–2c show the calculated pump light power evolutions along the fiber length and individual on/off Raman gain given by the five pump lights, respectively. The on/off Raman gain is defined as the ratio of the output signal light power with Raman pumping and without Raman pumping. From these two figures, it can be seen that the longest-wavelength pump (1501 nm) gives much greater gain than any other pumps. It not only gives most of the gain to the longer-wavelength signals, it also gives considerable gain (comparable to that contributed by the shortest-wavelength pump) to the shorter-wavelength signals. From FIG. 2b, it can also be found that the energy of the longest-wavelength pump can go much farther away from the fiber end than that of the shorter-wavelength pump (due to pump—pump interaction). Thus, the shorter-wavelength signals will see part of the gain from the shorter-wavelength pump, which is closer to the end of the fiber, and part of the gain from the longer-wavelength pump, which is more distributed along the fiber length. The longer-wavelength signals will see most of the gain from the longest-wavelength pump.
As discussed above, the noise originating from spontaneous Raman emission will increase when signal light frequency is closer to the pump light frequency under identical signal gain (refer to Equations 1 and 2), and a lumped gain closer to the fiber end will result in a worse noise performance than a distributed gain along the fiber length (refer to Equation 2). Accordingly, the noise performance in the shorter wavelength band is worse than that in the longer wavelength band, as is shown in FIG. 2a where the calculated gain (line 2), effective noise figure (NF) (line 1) and optical signal to noise ratio (OSNR) (line 3) for the above mentioned five-wavelength counter-pumped Raman fiber amplifier are shown. The effective NF, which is defined as the noise figure of the equivalent discrete amplifier, is given by
                              NF          eff                =                              1                          G                              on                /                off                                              ⁢                      (                          1              +                                                P                  ASE                                                                      E                    ph                                    ⁢                                      B                    0                                                                        )                                              (        3        )            where Gon/off is the on/off Raman gain, Eph is the signal photon energy and PASE is the noise power in a bandwidth B0. From the dashed line 1 in FIG. 2a it can be seen that the effective NF in the shorter wavelength band (1520 μm) can be more than 7 dB higher than that in the longer wavelength band (1610 nm). Because the attenuation curve of the fiber is not flat over 1520 nm to 1610 nm, to get a flat gain spectrum, the on/off Raman gain over this frequency range can be quite different for a span of 80 km Standard Single-Mode Fiber (SSMF) fiber. For example, the fiber loss at 1550 nm can be a little lower than 16 dB, but can be a little higher than 20 dB at 1610 nm. To obtain a flat gain spectrum, e.g., 0 dB, the on/off Raman gain needs to be 20 dB for a 1610 nm signal but only 16 dB for a 1550 nm signal. From Equation 3 it can be seen that, for a flat gain spectrum, the effective NF at 1610 nm can be 4 dB lower than that at 1550 nm even in the case that the OSNRs (i.e., the noise performance) at the two wavelengths are nearly identical. It is then clear that effective NF cannot be used as the measure of the noise performance over a large wavelength range as long as the fiber loss curve is not flat over this wavelength range. As a result, it is necessary to directly use the output OSNR (the input signal power should be identical for all the signal wavelengths) as the measure of noise performance in system design. The dotted line 3 in FIG. 2a gives the calculated output OSNR as a function of the signal wavelength. It can be observed that the output OSNR in the shorter-wavelength band can be nearly 3.5 dB lower than that in the longer wavelength band.
Two patent applications aiming at reduction of pump-induced four-wave mixing (FWM) effects were published recently (EP 1130825, Sep. 5, 2001, and EP 1130705, Sep. 5, 2001). In EP 1130705, pump—pump induced FWM effects are reduced at the expense of gain flatness by reducing the number of the pump lights used and shifting the FWM products to either the idle band between C-band and L-band or simply to the lower side of the signal bands. EP 1130825 deals with the pump-noise induced FWM effect (such an effect occurs when the zero dispersion frequency of the transmission fiber is centered between the pump frequency and a signal frequency experiencing a large Raman gain) but doesn't consider pump—pump induced FWM effects.
It would, therefore, be desirable to provide a method and apparatus for improving the noise performance of signals in long-haul and ultralong-haul transmission systems.